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# A palindrome is a number that reads the same backward or forward, for

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VP
Joined: 07 Dec 2014
Posts: 1217
A palindrome is a number that reads the same backward or forward, for  [#permalink]

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12 Nov 2017, 13:00
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Difficulty:

85% (hard)

Question Stats:

61% (03:06) correct 39% (02:51) wrong based on 117 sessions

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A palindrome is a number that reads the same backward or forward, for example 282 or 494. The first three digits of a five digit palindrome form a sequence of consecutive positive integers. If the sum of the five digits is equal to seven times the third digit, what is the sum?

A. 14
B. 21
C. 28
D. 35
E. 42
Math Expert
Joined: 02 Aug 2009
Posts: 8325
Re: A palindrome is a number that reads the same backward or forward, for  [#permalink]

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12 Nov 2017, 18:08
2
1
gracie wrote:
A palindrome is a number that reads the same backward or forward, for example 282 or 494. The first three digits of a five digit palindrome form a sequence of consecutive positive integers. If the sum of the five digits is equal to seven times the third digit, what is the sum?

A. 14
B. 21
C. 28
D. 35
E. 42

abcba....
a+b+c+b+a=7*c.......2(a+b)=6c....a+b=3c
Tells us that a and b are greater than c and sum of a and b is multiple of 3.
So a and b themselves are not MULTIPLE of 3

Possibility
210....no
543....5+4=3*3...yes
So Number is 54345
And sum is 7*3=21

B
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Director
Joined: 17 Dec 2012
Posts: 623
Location: India
A palindrome is a number that reads the same backward or forward, for  [#permalink]

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13 Nov 2017, 15:06
1
1
gracie wrote:
A palindrome is a number that reads the same backward or forward, for example 282 or 494. The first three digits of a five digit palindrome form a sequence of consecutive positive integers. If the sum of the five digits is equal to seven times the third digit, what is the sum?

A. 14
B. 21
C. 28
D. 35
E. 42

1. Write down the info
a+b+c+b+a= 7c
2a+2b+c=7c
a+b=3c

2. Fit values and find out
we see that 54345 is the palindrome.
So sum=21
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VP
Joined: 07 Dec 2014
Posts: 1217
A palindrome is a number that reads the same backward or forward, for  [#permalink]

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13 Nov 2017, 15:37
3
1
gracie wrote:
A palindrome is a number that reads the same backward or forward, for example 282 or 494. The first three digits of a five digit palindrome form a sequence of consecutive positive integers. If the sum of the five digits is equal to seven times the third digit, what is the sum?

A. 14
B. 21
C. 28
D. 35
E. 42

another approach:
let x=third digit
there are only two options:
1. x-2, x-1, x, x-1, x-2
7x=5x-6
x=-3 no
2. x+2, x+1, x, x+1, x+2
7x=5x+6
x=3 yes
7x=21
B
Intern
Joined: 09 Jun 2016
Posts: 24
Re: A palindrome is a number that reads the same backward or forward, for  [#permalink]

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21 Nov 2017, 23:25
1
gracie wrote:
gracie wrote:
A palindrome is a number that reads the same backward or forward, for example 282 or 494. The first three digits of a five digit palindrome form a sequence of consecutive positive integers. If the sum of the five digits is equal to seven times the third digit, what is the sum?

A. 14
B. 21
C. 28
D. 35
E. 42

another approach:
let x=third digit
there are only two options:
1. x-2, x-1, x, x-1, x-2
7x=5x-6
x=-3 no
2. x+2, x+1, x, x+1, x+2
7x=5x+6
x=3 yes
7x=21
B

Hi, I took the sequence as x, x+1 , x+2 , x+1 , x and got x=-5 , which is invalid since the sequence has positive numbers. In the second option that you took (x+2,x x+1.....), can we call the first 3 numbers consecutive? Technically a consecutive sequence should have +1 and not a -1 added to each subsequent number.
VP
Joined: 07 Dec 2014
Posts: 1217
A palindrome is a number that reads the same backward or forward, for  [#permalink]

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22 Nov 2017, 10:02
abhishek911 wrote:
gracie wrote:
gracie wrote:
A palindrome is a number that reads the same backward or forward, for example 282 or 494. The first three digits of a five digit palindrome form a sequence of consecutive positive integers. If the sum of the five digits is equal to seven times the third digit, what is the sum?

A. 14
B. 21
C. 28
D. 35
E. 42

another approach:
let x=third digit
there are only two options:
1. x-2, x-1, x, x-1, x-2
7x=5x-6
x=-3 no
2. x+2, x+1, x, x+1, x+2
7x=5x+6
x=3 yes
7x=21
B

Hi, I took the sequence as x, x+1 , x+2 , x+1 , x and got x=-5 , which is invalid since the sequence has positive numbers. In the second option that you took (x+2,x x+1.....), can we call the first 3 numbers consecutive? Technically a consecutive sequence should have +1 and not a -1 added to each subsequent number.

hi abhishek,
my understanding is that consecutive sequences can have either positive or negative differences,
gracie
Intern
Joined: 09 Jun 2016
Posts: 24
Re: A palindrome is a number that reads the same backward or forward, for  [#permalink]

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26 Nov 2017, 21:44
abhishek911 wrote:
gracie wrote:
gracie wrote:

Hi, I took the sequence as x, x+1 , x+2 , x+1 , x and got x=-5 , which is invalid since the sequence has positive numbers. In the second option that you took (x+2,x x+1.....), can we call the first 3 numbers consecutive? Technically a consecutive sequence should have +1 and not a -1 added to each subsequent number.

hi abhishek,
my understanding is that consecutive sequences can have either positive or negative differences,
gracie

Bunuel, can you help with this?
Manager
Joined: 06 Aug 2017
Posts: 78
GMAT 1: 570 Q50 V18
GMAT 2: 610 Q49 V24
GMAT 3: 640 Q48 V29
A palindrome is a number that reads the same backward or forward, for  [#permalink]

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03 Dec 2017, 10:45
abhishek911 wrote:
gracie wrote:
gracie wrote:

Hi, I took the sequence as x, x+1 , x+2 , x+1 , x and got x=-5 , which is invalid since the sequence has positive numbers. In the second option that you took (x+2,x x+1.....), can we call the first 3 numbers consecutive? Technically a consecutive sequence should have +1 and not a -1 added to each subsequent number.

hi abhishek,
my understanding is that consecutive sequences can have either positive or negative differences,
gracie

Hi

I will try to explain. May be it is helpful.

A sequence can be both increasing of decreasing, consequently we can take sequence either as a,a+1,a+2, ...... or a,a-1,a-2,......

Here in this case, the question stem mentions that sum of the items in the set = 7 times the middle term, this statement should ring a bell that the middle term may be smaller than the other terms, hence we took sequence as a, a-1, a-2,...., so that middle term can be made smaller.
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Joined: 09 Sep 2013
Posts: 13737
Re: A palindrome is a number that reads the same backward or forward, for  [#permalink]

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14 Jun 2019, 00:11
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Re: A palindrome is a number that reads the same backward or forward, for   [#permalink] 14 Jun 2019, 00:11
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